The EFT approach is not the only way of computing hereditary effects. An analogous derivation has been performed from the "Tutti Frutti" approach [1]}, [2]}, and presented in [3]}, and using PM techniques [4]}, [5]}, [6]}.
However, at 5PN order, the different results proposed [7]}, [8]}, [3]}, [4]} do not agree in the prediction of physical observables like the two-body scattering angle. The 5PN dynamics is not fully understood at the moment, and there are several subtle puzzles that needs to be studied and understood before proceeding in the evaluation of higher order PN corrections.
